seminar: Incompressible fluids with pressure, temperature and shear-rate dependent material coefficients
speaker: Josef Malek (Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute)abstract: We will deal with internal unsteady flows of a class of incompressible fluids with temperature, pressure and shear rate dependent viscosity that includes the Navier-Stokes-Fourier fluid as a special subclass.
We begin with a description of such fluids within the framework of a continuum, emphasizing the interesting departures of our model and its decsribtion from the classical fluid models and their formulations.
We then concentrate on mathematical analysis of three-dimensional unsteady flows of such fluids. We are interested in the issues connected with mathematical self-consistency of the models, i.e., we are interested in knowing whether 1) flows exist for reasonable, but arbitrary initial data and for all instants of time, 2) flows are uniquely determined, 3) the velocity is bounded.
The main part of the course will be focused on presentation of recently established results connected the first task.
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